Let events
A=Nathan has allergy
~A=Nathan does not have allergy
T=Nathan tests positive
~T=Nathan does not test positive
We are given
P(A)=0.75 [ probability that Nathan is allergic ]
P(T|A)=0.98 [probability of testing positive given Nathan is allergic to Penicillin]
We want to calculate probability that Nathan is allergic AND tests positive
P(T n A)
From definition of conditional probability,
P(T|A)=P(T n A)/P(A)
substitute known values,
0.98 = P(T n A) / 0.75
solving for P(T n A)
P(T n A) = 0.75*0.98 = 0.735
Hope this helps!!
Cannot see your image, but the formula for the volume of a sphere is
V=(4/3)πr³
to solve for r: r³=v÷(4/3)π=v*3/(4π)=3v/(4π) (three v out of 4 pi)
r=∛(3v/4π)
r equals the cubic root of (three v over 4π)
Draw a simple branch diagram to work the probabilities out.
You find that the chance of a poisonous mushroom is 0.08 and the chance of a red poisonous is 0.04.
So the probability that a poisonous mushroom is red is 1/2 or 0.5.
From the given function modeling the height of the ball:
f(x)=-0.2x^2+1.4x+7
A] The maximum height of the ball will be given by:
At max height f'(x)=0
from f(x),
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
thus the maximum height would be:
f(3.5)=-0.2(3.5)^2+1.4(3.5)+7
f(3.5)=9.45 ft
b]
How far from where the ball was thrown did this occur:
from (a), we see that at maximum height f'(x)=0
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
This implies that it occurred 3.5 ft from where the ball was thrown.
c] How far does the ball travel horizontally?
f(x)=-0.2x^2+1.4x+7
evaluationg the expression when f(x)=0 we get:
0=-0.2x^2+1.4x+7
Using quadratic equation formula:
x=-3.37386 or x=10.3739
We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.
Answer:
$2.96
Step-by-step explanation:
3x$2.67=$8.01
3x$2.73=$8.19
5x$3.27=$16.35
$8.01+$8.19+$16.35=$32.55
This makes 11 pounds of trail mix.
$32.55 divided by 11 = $2.9590909 = $2.96
